Earthquake_basemap

• 1. Data
• 2. $f(x)$
• 3. Haversine Fomula 사용한 거리 정의
• 4. Definition of a weighted adjacency matrix $W$
• 5. The weight edge function with temporal edge $(v_t,v_{t+1})$
• 6. Definition of Graph Laplacian matrix
• 7. Eigendecomposition
• 8. Principal components Analysis
• 2004, $n=571$
• 2005, $n=533$
• 2006, $n=512$
• 2007, $n=608$
• 2008, $n=508$
• 2009, $n=517$
• 2010, $n=560$
• 2011, $n=712$

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt 
import networkx as nx

import warnings
warnings.simplefilter("ignore", np.ComplexWarning)

!pip install haversine

Collecting haversine
  Downloading haversine-2.5.1-py2.py3-none-any.whl (6.1 kB)
Installing collected packages: haversine
Successfully installed haversine-2.5.1

from haversine import haversine

import time

1. Data

df = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/earthquakes-23k.csv')

_df = df.assign(Year=list(map(lambda x: x.split('/')[-1], df.Date))).query('Year>="2004" & Year<="2011"').reset_index().iloc[:,1:]

2. $f(x)$

f_true = np.array(_df.loc[:,"Magnitude"])

f = (f_true-f_true.mean())/f_true.std()

f@f ## SST 

4517.000000000005

(f-np.mean(f))@(f-np.mean(f)) ## SSE

4517.000000000003

(f*0-np.mean(f))@(f*0-np.mean(f)) ## SSH

3.022296055212013e-29

3. Haversine Fomula 사용한 거리 정의

locations = np.array(_df.iloc[:,[1,2]])

N = len(f)

dist_matrix = np.zeros((N,N))

for i in range(N):
    for j in range(i,N): 
        dist_matrix[i,j]=haversine(locations[i],locations[j])

dist_matrix = dist_matrix + dist_matrix.T

4. Definition of a weighted adjacency matrix $W$

$$W_{u,v}=\begin{cases}{exp(-\frac{[dist(u,v)]^2}{2\theta^2})} & \quad \text{if } dist(u,v) \leq κ \\ 0 & \quad \text{otherwise} \end{cases}$$

theta,kappa = 10000, 100000

W = np.exp( -(dist_matrix/20000)**2)

plt.hist(W.reshape(-1))

(array([ 261472.,  982186., 1180314., 1042392., 1435138., 1600586.,
        2109538., 2632908., 3587594., 5571161.]),
 array([0.36765227, 0.43088704, 0.49412181, 0.55735659, 0.62059136,
        0.68382613, 0.74706091, 0.81029568, 0.87353045, 0.93676523,
        1.        ]),
 <a list of 10 Patch objects>)

5. The weight edge function with temporal edge $(v_t,v_{t+1})$

$$W_{u_r,v_s}=\begin{cases} {W_{u,v}} & \quad \text{ if } u,v \in V_t \\ W_{u,v} \odot \beta & \quad \text{if }u=v \text{ and } r=s-1 \\ 0 & \quad \text{otherwise} \end{cases}$$

Nlst = _df.groupby("Year").aggregate(len).Date.tolist()
Nlst = np.cumsum(Nlst)

a=0
_beta =np.zeros((N,N))
for i in range(len(Nlst)):
    b=Nlst[i] 
    _beta[a:b,a:b]= np.ones(b-a)
    a=Nlst[i]

_W = W @ _beta

6. Definition of Graph Laplacian matrix

• $L = D - W$

D = np.diag(_W.sum(axis=1))

L = D - _W

7. Eigendecomposition

• ${\bf L} = {\boldsymbol\Psi} {\boldsymbol\Lambda} {\boldsymbol\Psi}^\top$

λ, Ψ = np.linalg.eig(L)

Λ = np.diag(λ)

8. Principal components Analysis

• $comp_k = f @ np.outer(Ψ[:,k], Ψ[:,k]) $
  • $k = 1, 2, 3, n$
• $p = \sum_{1}^{n} comp_{1}^{2},\sum_{1}^{n} comp_{2}^{2},…,\sum_{1}^{n} comp_{n}^{2}$
• $p = \frac{p}{\sum(p)}$

def p(i):
    return sum((f @ np.outer( Ψ[:,i], Ψ[:,i]))**2)

array_1 = np.array([p(i) for i in range(1,len(f))])
varprop = array_1/array_1.sum()
_index = pd.DataFrame({'index':range(1,len(f)),'varprop':varprop}).sort_values('varprop',ascending=False)
_indexlst = _index.iloc[:25,0].tolist()

_df["comp1"] = f @ np.outer( Ψ[:,0], Ψ[:,0])
_df["comp2"] = f @ np.outer( Ψ[:,_indexlst[0]], Ψ[:,_indexlst[0]])
_df["comp3"] = f @ np.outer( Ψ[:,_indexlst[1]], Ψ[:,_indexlst[1]])
_df["comp4"] = f @ np.outer( Ψ[:,_indexlst[2]], Ψ[:,_indexlst[2]])
_df["comp5"] = f @ np.outer( Ψ[:,_indexlst[3]], Ψ[:,_indexlst[3]])
_df["comp6"] = f @ np.outer( Ψ[:,_indexlst[4]], Ψ[:,_indexlst[4]])
_df["comp7"] = f @ np.outer( Ψ[:,_indexlst[5]], Ψ[:,_indexlst[5]])

from itertools import chain
def draw_map(m, scale=0.2):
    # draw a shaded-relief image
    m.shadedrelief(scale=scale)
    
    # lats and longs are returned as a dictionary
    lats = m.drawparallels(np.linspace(-90, 90, 13))
    lons = m.drawmeridians(np.linspace(-180, 180, 13))

    # keys contain the plt.Line2D instances
    lat_lines = chain(*(tup[1][0] for tup in lats.items()))
    lon_lines = chain(*(tup[1][0] for tup in lons.items()))
    all_lines = chain(lat_lines, lon_lines)
    
    # cycle through these lines and set the desired style
    for line in all_lines:
        line.set(linestyle='-', alpha=0.3, color='w')

!pip install Basemap

Collecting Basemap
  Downloading basemap-1.3.2-cp37-cp37m-manylinux1_x86_64.whl (862 kB)
     |████████████████████████████████| 862 kB 4.2 MB/s 
Requirement already satisfied: matplotlib<3.6,>=1.5 in /usr/local/lib/python3.7/dist-packages (from Basemap) (3.2.2)
Collecting pyproj<3.4.0,>=1.9.3
  Downloading pyproj-3.2.1-cp37-cp37m-manylinux2010_x86_64.whl (6.3 MB)
     |████████████████████████████████| 6.3 MB 63.9 MB/s 
Requirement already satisfied: six<1.16,>=1.10 in /usr/local/lib/python3.7/dist-packages (from Basemap) (1.15.0)
Requirement already satisfied: numpy<1.23,>=1.21 in /usr/local/lib/python3.7/dist-packages (from Basemap) (1.21.5)
Collecting pyshp<2.2,>=1.2
  Downloading pyshp-2.1.3.tar.gz (219 kB)
     |████████████████████████████████| 219 kB 73.4 MB/s 
Collecting basemap-data<1.4,>=1.3.2
  Downloading basemap_data-1.3.2-py2.py3-none-any.whl (30.5 MB)
     |████████████████████████████████| 30.5 MB 101.1 MB/s 
Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib<3.6,>=1.5->Basemap) (1.4.0)
Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib<3.6,>=1.5->Basemap) (0.11.0)
Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib<3.6,>=1.5->Basemap) (3.0.7)
Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib<3.6,>=1.5->Basemap) (2.8.2)
Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from kiwisolver>=1.0.1->matplotlib<3.6,>=1.5->Basemap) (3.10.0.2)
Requirement already satisfied: certifi in /usr/local/lib/python3.7/dist-packages (from pyproj<3.4.0,>=1.9.3->Basemap) (2021.10.8)
Building wheels for collected packages: pyshp
  Building wheel for pyshp (setup.py) ... done
  Created wheel for pyshp: filename=pyshp-2.1.3-py3-none-any.whl size=37324 sha256=df866092e9544143c5396a484dfb9044cd16f234af9410afb05e994ac18fd1bf
  Stored in directory: /root/.cache/pip/wheels/43/f8/87/53c8cd41545ba20e536ea29a8fcb5431b5f477ca50d5dffbbe
Successfully built pyshp
Installing collected packages: pyshp, pyproj, basemap-data, Basemap
Successfully installed Basemap-1.3.2 basemap-data-1.3.2 pyproj-3.2.1 pyshp-2.1.3

from mpl_toolkits.basemap import Basemap

m = Basemap(projection='cyl', resolution=None,
            llcrnrlat=-90, urcrnrlat=90,
            llcrnrlon=-180, urcrnrlon=180)

2004, $n=571$

_G1 = nx.Graph(_W[:len(_df.query('Year<="2004"')),:len(_df.query('Year<="2004"'))]-np.identity(len(_df.query('Year=="2004"'))))
_pos1 = nx.spring_layout(_G1,iterations=20)
m_pos1 = list(zip(_df.query('Year=="2004"').Longitude,_df.query('Year=="2004"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp2,node_size = np.abs(_df.query('Year=="2004"').comp2)*10000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp3,node_size = np.abs(_df.query('Year=="2004"').comp3)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp4,node_size = np.abs(_df.query('Year=="2004"').comp4)*200, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp5,node_size = np.abs(_df.query('Year=="2004"').comp5)*25000, ax=ax,cmap='bwr', alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp6,node_size = np.abs(_df.query('Year=="2004"').comp6)*5000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G1,m_pos1,node_color=_df.query('Year=="2004"').comp7,node_size = np.abs(_df.query('Year=="2004"').comp7)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2005, $n=533$

_G2 = nx.Graph(_W[len(_df.query('Year<="2004"')):len(_df.query('Year<="2005"')),len(_df.query('Year<="2004"')):len(_df.query('Year<="2005"'))]-np.identity(len(_df.query('Year=="2005"'))))
_pos2 = nx.spring_layout(_G2,iterations=20)
m_pos2 = list(zip(_df.query('Year=="2005"').Longitude,_df.query('Year=="2005"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp1,node_size=50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp2,node_size = np.abs(_df.query('Year=="2005"').comp2)*10000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp3,node_size = np.abs(_df.query('Year=="2005"').comp3)*250, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp4,node_size = np.abs(_df.query('Year=="2005"').comp4)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp5,node_size = np.abs(_df.query('Year=="2005"').comp5)*100000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp6,node_size = np.abs(_df.query('Year=="2005"').comp6)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G2,m_pos2,node_color=_df.query('Year=="2005"').comp7, node_size = np.abs(_df.query('Year=="2005"').comp7)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2006, $n=512$

_G3 = nx.Graph(_W[len(_df.query('Year<="2005"')):len(_df.query('Year<="2006"')),len(_df.query('Year<="2005"')):len(_df.query('Year<="2006"'))]-np.identity(len(_df.query('Year=="2006"'))))
_pos3 = nx.spring_layout(_G3,iterations=20)
m_pos3 = list(zip(_df.query('Year=="2006"').Longitude,_df.query('Year=="2006"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp1,node_size=50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp2,node_size = np.abs(_df.query('Year=="2006"').comp2)*10000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp3,node_size = np.abs(_df.query('Year=="2006"').comp3)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp4,node_size = np.abs(_df.query('Year=="2006"').comp4)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp5,node_size = np.abs(_df.query('Year=="2006"').comp5)*5000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp6,node_size = np.abs(_df.query('Year=="2006"').comp6)*2000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G3,m_pos3,node_color=_df.query('Year=="2006"').comp7,node_size = np.abs(_df.query('Year=="2006"').comp7)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2007, $n=608$

_G4 = nx.Graph(_W[len(_df.query('Year<="2006"')):len(_df.query('Year<="2007"')),len(_df.query('Year<="2006"')):len(_df.query('Year<="2007"'))]-np.identity(len(_df.query('Year=="2007"'))))
_pos4 = nx.spring_layout(_G4,iterations=20)
m_pos4 = list(zip(_df.query('Year=="2007"').Longitude,_df.query('Year=="2007"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp2,node_size = np.abs(_df.query('Year=="2007"').comp2)*25000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp3,node_size =np.abs(_df.query('Year=="2007"').comp3)*25000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp4,node_size = np.abs(_df.query('Year=="2007"').comp4)*25000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp5,node_size = np.abs(_df.query('Year=="2007"').comp5)*1000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp6,node_size = np.abs(_df.query('Year=="2007"').comp6)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G4,m_pos4,node_color=_df.query('Year=="2007"').comp7,node_size = np.abs(_df.query('Year=="2007"').comp7)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2008, $n=508$

_G5 = nx.Graph(_W[len(_df.query('Year<="2007"')):len(_df.query('Year<="2008"')),len(_df.query('Year<="2007"')):len(_df.query('Year<="2008"'))]-np.identity(len(_df.query('Year=="2008"'))))
_pos5 = nx.spring_layout(_G5,iterations=20)
m_pos5 = list(zip(_df.query('Year=="2008"').Longitude,_df.query('Year=="2008"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp2,node_size = np.abs(_df.query('Year=="2008"').comp2)*25000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp3,node_size = np.abs(_df.query('Year=="2008"').comp3)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp4,node_size = np.abs(_df.query('Year=="2008"').comp4)*5000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp5,node_size = np.abs(_df.query('Year=="2008"').comp5)*100000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp6,node_size = np.abs(_df.query('Year=="2008"').comp6)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G5,m_pos5,node_color=_df.query('Year=="2008"').comp7,node_size = np.abs(_df.query('Year=="2008"').comp7)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2009, $n=517$

_G6 = nx.Graph(_W[len(_df.query('Year<="2008"')):len(_df.query('Year<="2009"')),len(_df.query('Year<="2008"')):len(_df.query('Year<="2009"'))]-np.identity(len(_df.query('Year=="2009"'))))
_pos6 = nx.spring_layout(_G6,iterations=20)
m_pos6 = list(zip(_df.query('Year=="2009"').Longitude,_df.query('Year=="2009"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp2,node_size = np.abs(_df.query('Year=="2009"').comp2)*50000,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp3,node_size = np.abs(_df.query('Year=="2009"').comp3)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp4,node_size = np.abs(_df.query('Year=="2009"').comp4)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp5,node_size = np.abs(_df.query('Year=="2009"').comp5)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp6,node_size = np.abs(_df.query('Year=="2009"').comp6)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G6,m_pos6,node_color=_df.query('Year=="2009"').comp7,node_size = np.abs(_df.query('Year=="2009"').comp7)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2010, $n=560$

_G7 = nx.Graph(_W[len(_df.query('Year<="2009"')):len(_df.query('Year<="2010"')),len(_df.query('Year<="2009"')):len(_df.query('Year<="2010"'))]-np.identity(len(_df.query('Year=="2010"'))))
_pos7 = nx.spring_layout(_G7,iterations=20)
m_pos7 = list(zip(_df.query('Year=="2010"').Longitude,_df.query('Year=="2010"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp2,node_size = np.abs(_df.query('Year=="2010"').comp2)*500,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp3,node_size = np.abs(_df.query('Year=="2010"').comp3)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp4,node_size = np.abs(_df.query('Year=="2010"').comp4)*2500, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp5,node_size = np.abs(_df.query('Year=="2010"').comp5)*25000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp6,node_size = np.abs(_df.query('Year=="2010"').comp6)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G7,m_pos7,node_color=_df.query('Year=="2010"').comp7,node_size = np.abs(_df.query('Year=="2010"').comp7)*10000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

2011, $n=712$

_G8 = nx.Graph(_W[len(_df.query('Year<="2010"')):len(_df.query('Year<="2011"')),len(_df.query('Year<="2010"')):len(_df.query('Year<="2011"'))]-np.identity(len(_df.query('Year=="2011"'))))
_pos8 = nx.spring_layout(_G8,iterations=20)
m_pos8 = list(zip(_df.query('Year=="2011"').Longitude,_df.query('Year=="2011"').Latitude))

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp1,node_size = 50, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp2,node_size = 50,ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp3,node_size = np.abs(_df.query('Year=="2011"').comp3)*50000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp4,node_size = np.abs(_df.query('Year=="2011"').comp4)*25000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp5,node_size = np.abs(_df.query('Year=="2011"').comp5)*100000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp6,node_size = np.abs(_df.query('Year=="2011"').comp6)*25000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)

fig,ax = plt.subplots(figsize = (16,8))
draw_map(m)
nodes = nx.draw_networkx_nodes(_G8,m_pos8,node_color=_df.query('Year=="2011"').comp7,node_size = np.abs(_df.query('Year=="2011"').comp7)*1000, ax=ax,cmap='bwr',alpha=0.5)
plt.colorbar(nodes)
plt.axis()
ax.set_axis_on()
ax.tick_params(left=True, bottom=True, labelleft=True, labelbottom=True)